Results on invariance-based feedback control for hybrid dynamical systems

Chai, Jun; Sanfelice, Ricardo G.

doi:10.1109/cdc.2016.7798338

Cited by 1 publication

(5 citation statements)

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“…More precisely, the results in [29] are derived from sufficient conditions for forward invariance of generic sets 14 and are not tailored to sublevel sets of V. In particular, in [29], to guarantee that the state component of every solution pair remains in M r , the feedback law κ c needs to be locally Lipschitz, see [29,Theorem 4.7,R4)]. To get such a property, condition [29, Theorem 4.7, R1')] 14 The equivalent results of Corollary 3.6 in Section III.…”

Section: Since For Everymentioning

confidence: 94%

“…which is greater than 2γ ε 2 + h min since γ ε 2 + h min < e 1 √ E max . Then, 3.6.2) holds for every x ∈ M r ∩ Π d (D 2 ) since (29).…”

Section: Remark 323mentioning

confidence: 95%

“…Since (32) and the fact that ρ c (x) is positive for every x ∈ M c , ∇V (x), ξ < 0, for every x ∈ M c and ξ ∈ F u,w (x, κ c (x), 0). Then, (19) and 34 More precisely, the results in [29] are derived from sufficient conditions for forward invariance of generic sets 14 and are not tailored to sublevel sets of V. In particular, in [29], to guarantee that the state component of every solution pair remains in M r , the feedback law κ c needs to be locally Lipschitz, see [29,…”

Section: Remark 318mentioning

confidence: 99%

“…Moreover, item 3.17.4) ensures completeness of every (φ, w) ∈ SH w (M r ). Remark 3.22: Results about selecting feedbacks from regulation maps for nominal hybrid systems (without perturbations), developed using a different set conditions and notion of control Lyapunov functions for forward invariance appeared in [29]; see details in [29,Definition 4.1].…”

Section: Since For Everymentioning

confidence: 99%

“…The nominal version of the results in this paper appeared without proof in the conference article[29] with a slightly different definition of the CLF for forward invariance.…”

mentioning

confidence: 99%

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Forward Invariance of Sets for Hybrid Dynamical Systems (Part II)

Chai

Sanfelice

2021

IEEE Trans. Automat. Contr.

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This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a control law if every solution to the closed-loop system that starts from the set stays within the set for all future time, regardless of the value of the disturbances. Building on the first part of this article, which focuses on analysis (Chai and Sanfelice, 2019), in this article, sufficient conditions for generic sets to enjoy such a property are proposed. To construct invariance inducing state-feedback laws, the notion of robust control Lyapunov function for forward invariance is defined. The proposed synthesis results rely on set-valued maps that include all admissible control inputs that keep closed-loop solutions within the set of interest. Results guaranteeing the existence of such statefeedback laws are also presented. Moreover, conditions for the design of continuous state-feedback laws with minimum point-wise norm are provided. Major results are illustrated throughout this article in a constrained bouncing ball system and a robotic manipulator application.

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Section: Since For Everymentioning

confidence: 94%

“…which is greater than 2γ ε 2 + h min since γ ε 2 + h min < e 1 √ E max . Then, 3.6.2) holds for every x ∈ M r ∩ Π d (D 2 ) since (29).…”

Section: Remark 323mentioning

confidence: 95%

Section: Remark 318mentioning

confidence: 99%

Section: Since For Everymentioning

confidence: 99%

“…The nominal version of the results in this paper appeared without proof in the conference article[29] with a slightly different definition of the CLF for forward invariance.…”

mentioning

confidence: 99%

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